Extensional Schemes of Multipartite Non-interactive Key Exchange from Multilinear Maps

Key agreement is a fundamental primitive in cryptography and the question of generalizing the celebrated 2 party non-interactive key exchange, Diffie-Hellman protocol, to a multipartite setting was left as an important open problem. Boneh and Silverberg proposed the notion of multilinear maps for the first time in 2003 and put forward a theoretical construction of multipartite non-interactive key exchange protocol from multilinear maps. In their protocol, however, the number of users N and the multilinearity k are related by N=k+1, resulting in the system initializing another multilinear map when the number of users who want to exchange a session key changes. In this paper, we describe two extensional schemes, which enables any less than or equal to N users derive a common shared key from an (N-1)-multilinear map. In addition, using our extensional schemes, we show a concrete scenario: The establishment of any discussion group in a user group. Furthermore, we analyze its security.